A spring has spring constant 0.3 m/newton. What force is necessary to stretch the spring by 1.5 meters? Use Hooke's Law, F = kx. Show all your steps.

Answer 1

To find the force necessary to stretch a spring by a certain distance, we can use Hooke's Law, which is given by the formula:

\[ F = kx \]

Where:

• \( F \) is the force applied to the spring (in Newtons),
• \( k \) is the spring constant (in Newtons per meter),
• \( x \) is the extension or compression of the spring from its equilibrium position (in meters).

In this problem:

• The spring constant \( k = 0.3 , \text{N/m} \),
• The extension \( x = 1.5 , \text{m} \).

Now we can substitute the values of \( k \) and \( x \) into Hooke's Law to find the force \( F \).

1. Substitute the values into the equation:

\[ F = 0.3 , \text{N/m} \times 1.5 , \text{m} \]

2. Perform the multiplication:

\[ F = 0.3 \times 1.5 = 0.45 , \text{N} \]

Therefore, the force necessary to stretch the spring by 1.5 meters is:

\[ F = 0.45 \text{ Newtons} \]